Exponential factorizations of holomorphic maps
Copyright policy )Exponential factorizations of holomorphic maps
We show that any element of the special linear group $SL_2(R)$ is a product of two exponentials if the ring $R$ is either the ring of holomorphic functions on an open Riemann surface or the disc algebra. This is sharp: one exponential factor is not enough since the exponential map corresponding to $SL_2(\mathbb{C})$ is not surjective. Our result extends to the linear group $GL_2(R)$.
9 pages
- University of Bern Switzerland
- Complutense University of Madrid Spain
factorization of matrices, Mathematics - Complex Variables, matrices of holomorphic functions, disk algebra, Algebras of analytic functions of one complex variable, Matrix exponential and similar functions of matrices, Riemann surfaces, exponential matrices, Matrices over function rings in one or more variables, FOS: Mathematics, 15A54, 15A16, 30H50, 32A38, 32E10, 48E25, Complex Variables (math.CV)
factorization of matrices, Mathematics - Complex Variables, matrices of holomorphic functions, disk algebra, Algebras of analytic functions of one complex variable, Matrix exponential and similar functions of matrices, Riemann surfaces, exponential matrices, Matrices over function rings in one or more variables, FOS: Mathematics, 15A54, 15A16, 30H50, 32A38, 32E10, 48E25, Complex Variables (math.CV)
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